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Restricted orbit identification

3. Problems with the linear theory

The linear theory for orbit identification provides the most rigorous mathematical setting to solve this problem. A mathematical theorem, however, is not at all a rigorous tool unless all the hypothesis are applicable to the concrete problem to be solved. The hypothesis needed to apply the formalism of Section 2 are the following:

- 1.
- The normal matrices and are invertible and positive-definite.
- 2.
- The map between the space of the residuals and the space of estimated parameters is in the linear regime, that is the linearized map is a good approximation in a region including both orbits.
- 3.
- The observation errors are of a size consistent with the residual normalization adopted.

In this Section we shall discuss the applicability of these three hypothesis to the problem of orbit identification.

1999-05-20